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Full text of "The Schema Axiom as Foundation of a Theory for Measurement and Rrepresentation of Consciousness"

ISSN 0281-9864 



The Schema Axiom 

as Foundation of a Theory 

for Measurement and Representation 

of Consciousness 

Bernhard Bierschenk 



1991 



No. 38 




Copenhagen University 
Denmark 




Lund University 
Sweden 



KOGNITIONSVETENSKAPLIG 
FORSKNING 

Cognitive Science Research 



The Schema Axiom 

as Foundation of a Theory 

for Measurement and Representation 

of Consciousness 

Bernhard Bierschenk 



1991 



No. 38 



Cognitive Science Research 

Lund University 
Sweden 



Postal address 



Editor 



Adm. editor 



Cognitive Science Research 
P.O. Box 7080 
S-220 07 LUND 
SWEDEN 



Bernhard Bierschenk 
Department of Psychology 
Lund University 



Helge Helmersson 
Department of Business Adm. 
Lund University 



Abstract 

For the first time in the history of psychological and educational measurement the 
Kantian schema has been applied to natural language expression in a rigourous and 
precise way. The crucial novelty of the approach concerns the way in which the 
Kantian schema interrelates the analytic with the synthetic mode in the construction of 
the presented formalism. The main thesis advanced is based on the premise that the 
synthetic in contrast to the analytic proposition plays the central role in the 
measurement and representation of consciousness. It is assumed that the 
discontinuities in natural language production are the only reliable observations and 
that there is at present no other way in which these observations can be formalized. 
Despite the enormous number of textual elements and great variations, it has been 
possible to demonstrate empirically perspective and objective structures as the result 
of a series of nondeterministic bifurcations of a dynamic vector field within Euclidean 
space. By contrasting the Caption to the picture series of the original Visual Cliff 
experiments with a narration produced in a single subject experiment, it was possible 
to show that the formalism has the capacity of dealing with alternative descriptions of 
one and the same system (experimental arrangement). On the basis of the given 
theoretical outline, a totally new apprehension of 'text' and of the underlying 
theoretical concepts related to the ecological approach to visual perception has 
emerged. 



The classical and basic approach to the study of behaviour rests on the 
proposition that the measurement and representation of sequences of extraordinary or 
important behavioural events (Y) is possible if a given organism (X) induces a dynam- 
ics, i.e. a change of state. If X observes the event Y' after the event Y then X will 
show a tendency to expect Y' whenever Y appears. Consequently, there is no room for 
modelling intentionality nor for modelling thinking. "Intentionality is still one of the 
most elusive of all notions" (Kugler & Turvey, 1987, p. xiv). 

The original meaning of this most primitive and clumsy but persistent method 
is to model the choice of the organism on which of two actions should be carried out. 
An elaboration of the method into preference or public choice models is simply an 
extension of a "sense of number" which is characteristic of all higher order nervous 
systems (Danzig, 1968, pp. 1-12). Thus, every observable behaviour can be regarded 
as an instant of a mapping from a stable state to a number (one, zero). Because an 
omen such as "If X does Y and X causes Y then X wants Y" is a special example of 
the behaviour principle although expressed in language, it can be concluded that the 
omen, i.e. behavioural semantics, has its origin in animal nature. Behavioural se- 
mantics is concerned with a precise attribution of a cause to a behavioural event. With 
the results obtained from both informal and formal demonstrations it is possible to 
conclude that (1) conditional judgment (if-then anticipation), (2) classification 
(generalization) and (3) comparison (combination) are primitive functions pertaining 
to the logic of behavioural semantics, i.e. the logic of the organism. These elementary 
processes are, according to Piaget (1978, p. 94) "not intentionally organized and used 
by an individual subject with a specific new solution in view". 

The classical theories of behaviour build on the significance of psychological 
pain or bereavement in behaviour reinforcement. Reward and punishment are used as 
the generally accepted steering and control mechanism of human and social 
development. The construction of appropriate models has been based on the 
conviction that "believes" are the result of fundamental psychological processes. The 
following basic assumptions of psychophysics constitute the generalized foundation of 
all models of behaviour and behavioural semantics: 

(1) the individual avoids/wants objects or events 

(2) preferences are persistent 

(3) stable preferences are generalizable 

(4) changes in behaviour cause changes in preferences 

(5) preferences and behaviour are independent, i. e. only associatively related. 

The traditional basis of investigating choice behaviour is a formal definition. 
By comparing the elements of a set of attainable alternatives the individual's judgment 
of intensity in a belief is described with respect to the transitivity, reflexivity, and 
completeness of the relations holding between the elements of the set. The following 
four basic parameters are of significance for an operationalization of a person's way of 
making rational decisions: 

(1) experience of intensity in wanting or avoidance 

(2) range of variation in the tolerance of risk taking 

(3) threshold value of excitability, and 

(4) observable differences. 



These parameters have also found widespread acceptance as foundation of 
research on consciousness and cognitive research in general due to the very attractive 
logic of association. Behaviourally, it implies that pleasure as its momentum is 
expressed not as product (like the momentum in physics) but as a difference in the 
maximization of utility. From this argumentation two further assumptions can be 
derived immediately: 

(1) the efficiency of a particular individual defines the success (risk taking and gain) 
of a certain behaviour strategy, and 

(2) hierarchic organizations have to be designed such that they preserve individual 
growth and distributive justice. 

This axiomatic foundation has been developed with the purpose to generate 
value-free sets of data and to guarantee the generalizability of empirical results. The 
axiom of number is the foundation of any physical theory of behaviour and knowledge 
of behaviour is defined as the formal structure of the product of inquiry. In this sense, 
the knower is an ideal and abstracted individual who cannot know objects with 
certainty because of their indeterminacy. Though, the world is knowable to the extent 
that it is itself a formal structure which is computationally accessible within the 
boundaries of formal-logical calculation. All cognition is computational, mainly on 
the basis of extensional logics and models of geometry and kinematics. Knowledge is 
limited but rational, because of its relationship to formal logics. 

The Measurement of Change 

Complex models have been developed for simulating choice behaviour in 
complex situations. "Intelligent structuring" and "flexible organization" are two key 
concepts in the design and implementation of appropriate computer programs. Change 
is thereby defined as the difference between more or less transparent variables and 
their interconnections. It seems that "intelligent structuring" gives expression to the 
designer's ability to construct precise and rigid formalizations of his assumptions of 
motion perception. On the other hand, "flexible organization" reflects his ability to 
construct changeable databases. Moreover, the interaction of both concepts allows for 
a high degree of formal system control in the processing of information. The 
algorithmic foundation of choice behaviour is justified on the grounds that it has been 
possible to construct an isomorphic relation between symbolic logic and arithmetics. 
Through this isomorphism, formal logics based on the analytic proposition could be 
given the form of arithmetic procedures. As a consequence, a number of syllogisms 
could be computed through completely automatized procedures. This manipulation of 
logical formulas has been taken as a pretext for the hypothesis that humans should 
have computable knowledge about the adequate behavioural response in situations of a 
certain kind of complexity. For example, Becker (1973) has presented a computer 
model for the simulation of "experience" as foundation of the avoidance of "Falling- 
off-places". As argued in Bierschenk (1984), the focus is on an organized complexity 
implying the collection and conditioning of S-R bonds, techniques which give the 
impression of a strict environmentalism. To be sure, Becker's simulated behaviour of 
an organism on a Cliff shows that the organism has the capacity to adapt its action to 
its environment. But it does so without the inborn ability of spontaneous self- 
preservation of an infant of only a few weeks of age. 



To summarize, a computer simulation or any other simulation of awareness is 
characterized by: 

(1) a great number of state variables 

(2) a manifold of state variations 

(3) variations in degree of transparency 

(4) a high degree of interconnectivity 

(5) eigendynamics of some variables 

(6) eigendynamics of a complex of variables 

(7) a possibility of satisfying contradictory goal variables. 

Different high-level computer languages entail partly different variables for the 
organization of complex problem solving situations. However, the development of an 
ever greater computing capacity goes hand in hand with the development of ever more 
powerful high-level languages. Within this development, the mental dimension is 
conceived as cognitive processes, which have to be explained with reference to 
"schemas" in Minsky's (1975) sense. They are a means for the representation of world 
knowledge. However, when a system configuration builds on the imperative of 
association, "learning" is modelled on the basis of already known information 
(Bierschenk, 1984). Thus, a cognitive mechanism of this type would be capable of 
inferring "similarity" and establish "boundary conditions", but would be incapable of 
judgment, i. e. prospective reference. Informative components can be extracted, if and 
only if uniqueness can be detected or if known information can be transformed by op- 
erations of a schematizing process in the Kantian sense. 

The Kantian Schema 
Basically, the schematizing process merges the empirical with the formal 
aspect of an evolving system (Hartman, 1967, pp. 101-102). The crystallization of a 
system means always the discovery of a logic. Consequently, schematization implies 
that the empirical phenomenon under study needs to be connected with an application 
of logic. The fundamental assumption underlying classical argumentation in philoso- 
phy and science is that natural language is an insufficient instrument for the detection 
of the "true" nature of the world. For this reason, philosophers, logicians, and 
mathematicians had to invent pure elements and relations holding between them. By 
manipulating formulas assumed to correspond to the real world, it would then be 
possible to determine, within a model world, what is true and what is false. In this way 
formal logics would be a promising tool in the description of natural phenomena. The 
unreasonable success of mathematics with respect to physics (Wigner, 1967, p. 171) 
has been taken as a pretext by logic oriented linguists to give natural language 
expressions a semantic logical definition and thus, to describe language with reference 
to sets of analytical propositions. 

The Analytical Proposition 

The analytical proposition gives a formal structural definition of the clause or 
part of it. A clause consists of a subject and a predicate associatively connected 
through a copula, usually 'is'. The connotations of the proposition contain the 
instructions for the intentional use of a particular term. The way in which a term has to 
be used is prescribed by the denotations established through syntactic rules. In Kantian 
terms, this is the foundation of an analytic proposition. The analytical proposition is at 
hand whenever the predicate is contained (maybe in a covert way) in the subject. The 



ability to abstract the connotations of an analytic proposition is given through the 
ability to generate analytical concepts. These are the abstractions of experience, real or 
conceived. One of Kant's analytic propositions frequently cited is: 

A triangle is a three- sided figure (1) 

The expression (1) is analytic, since the term 'triangle' can be substituted with 'a three- 
sided figure' each time an identity relation is established within a closed system, i. e. 
the mechanism of symbolic logic. Thus, "analytic concepts are those whose intensions 
consist of predicates" (Hartman, 1967, p. 31) which may be defined as "a set of words 
or symbols" (Craik, 1943, p. 29) which by definition must be a closed set. Every 
analytic concept derived by generating a set is surrounded by a "cloud of intensions" 
(Hartman, 1967, p. 34) which gives meaning to the concept. Logically, the inde- 
pendence between an analytic concept and its manifold of interpretations constrains its 
scientific power. Only through a continuously repeated process of abstraction can 
analytic concepts be redefined and possibly purified. What is lost in this process is 
meaning. Hartman (1967, p. 34) writes: 

"The analytic definition seen in analytic purity is like an iceberg whose larger portion, 
the process of generalization is submerged." 

Kant declared that the connotations of the predicate which are contained in 
those of the subject must lead to analytical propositions. From the classical 
behavioural point of view, the subject is the perceiver and the perceiver's language is 
the medium in which the structure of the subjective world of experience and the 
structure of the objective world show structural identity. Here, the language of the 
immaterial and the material describe two complementary aspects of one and the same 
reality. Though, the relationship between the perceiver and the perceived is not a 
causal but an identity relation. Therefore, the original studies of consciousness at the 
turn of the 19th century have focused on the analytical model as the psychological 
model in which the isomorphism between the predicate (the perceptible world) and the 
subject (the mental world) appears through an identity relation. 

The Synthetic Proposition 

In contradistinction, Kant formulated the synthetic proposition and declared 
that meaning can be comprehended only in synthetic terms. The significance of the 
synthetic proposition rests on the concept of linkage. Linkage implies that the 
predicate is linked with the subject. As such the predicate is neither thought to be part 
of the subject nor to be analysable out of the subject (Kant, 1975, p. 110-112). The 
concept of linkage signals "predictive ability" (Rosen, 1978, p. 84), and thus novelty. 
Transformed into a psychological model for the study of consciousness, the synthetic 
proposition can be given the following expression: 

(int(A))a(ort(0)) (2) 

The first bracketed expression denotes that intention operates. Intention signifies a 
course of action. It implies a stretching out (Latin: intentio) or a stretching toward 
(Latin: intendere) some objective. To incorporate the intentional component into the 
expression (2) implies that the scope of action within a particular environment is the 
indispensable part. Intention is necessary for an organism (A) to act purposely. This is 



indicated by the cooperative actions (a). The second bracketed expression indicates the 
importance of the ability to orientate (ort) toward some object(ive) (O). Observing 
behaviour (a) in individuals acting purposely in a meaningful environment is hardly 
possible without an organism's expression of an 'intended and 'oriented' 
schematization. In behavioural science terms, this means that psychological 
phenomena must be conceived as meaningful actions carried out by an Agent. Acting 
purposely presupposes not only that structure can be detected but also that 
intentionality and orientation can be observed. This may be illustrated by the natural 
language expression: 

The researchers observed infants (3) 

The variables in the expression (3) may be regarded as describing an observation 
belonging to a scientific environment. The researchers are the agents who perform a 
series of actions and the infants are the experimental subjects who function as the 
object(ive) of observation and study. Given that the relationship holding between 
researchers and infants has emerged the expression signifies "unity" in Polanyi and 
Prosch's (1975, pp. 66-81) sense on the basis of differentiated and transformed per- 
ception and behaviour. However, a researcher may place himself in the position of the 
objective: 

I observe that I study myself (4) 

The transformative process initiated by this expression (4) shows that the relation 
between Agent and Objective emerges as the smallest common denominator when 
both reside in the same organism. Further, The reader of such a text may be placed in 
the observer's position close to the occurring event. The A-component in the 
expression (4) indicates that intention operating at the observation and action level can 
be distinguished. At the observation level it gives expression to a distance at the same 
time as the necessary cooperative action and adaptation to the empirical observation is 
ensured. What is synthesized are the objects of nature kept together by the logic of 
affinity which guarantee the necessary synthetic unity of appearance. What Kant calls 
"lex continui in natura" (Cassirer, 1970, p. 48) is kept together by the transcendental 
logic of the Schema. For the behaving organism variance in the environment makes 
possible self-reference through "immediate awareness" (Kant, 1975) or "direct per- 
ception" (Gibson, 1979) of the invariance of objects and events. 

If, for example, it may be assumed that infants represent the phenomenon of 
development rather their behaviour or function within events is being studied. The 
phenomenon, the scientific focus, is being elucidated through the infants acting toward 
certain specific objectives: 

Researchers observed that infants crawled over edges (5) 

A a (0)(a a O) 

The researchers observations are composed of a series of (AaO) relations manifesting 
themselves in a hierarchy. When is comes to represent those observations this is con- 
tinuously done in the form of a process, that is, the observations are packed 
linguistically coherent. The product is some form of running text. In general, any 
awareness that can be formalized into the expression 



(Aa(AaO)) 



(6) 



is an expression of a purposive act. Kant used the schema notion as device for 
establishing the scope of action by relating the events stretching over series of 
instances ("Segmente einer Zeitreihe") (Bierschenk, 1981). The schematizing process 
is assumed to achieve a synthesis by which variety becomes specified and symbolized. 
This means that the perceiver-perceived relations are accounted for on the basis of 
unity signified by symbols. As a consequence, information processing in absence of 
natural language is inaccessible to consciousness. In the following it will be shown 
that consciousness can be measured and represented only through natural language 
production. 

General Systems Expression 

A fundamental fact of all living systems is that they are self -referential and 
thus, they contain their own descriptions (Pattee, 1977, 1980). In operation, self-refer- 
entiality makes use of the dual steering and control mechanism exerted by the (A) and 
(O) of the expression (2). 

In Kantian terminology the syntax of the expression constitutes a schema, i. e. 
the empirical independent (AaO) formula. The formula has axiomatic properties in 
that, it generates a formal system. Modelling and unfolding the formula into a system 
is carried out by a series of empirical dependent (AaO) relations and indicated by the 
index i, i = 1, 2, 3, ..., n. The following relations constitute the architectural config- 
uration of the system: 



General systems expression: (AaO) = A a O , where 



(7) 



a = Dictionary identification of textual strings 



Component Substitution 

A n Textual strings 

A n X-variable 

A n A n _i 

A n An.x + On.i 

A n X-variable 

O n Textual strings 

O n Y-variable 

On A n+1 + °n+l 



Condition 

A n is directly accessible 

A n is covert and unknown 

A n is indirectly accessible 

A n = 'it' and (AaO) n _i exists 

A n = 'it' and (AaO) n _i does not exist 

O n is direcly accessible 
O n is unknown 
O n is indirectly accessible and 
(AaO) n+ i exists 



In general, a set of verbal strings has been defined as a clause if and only if all three 
constitutive components are present. In principle, an agent dummy (A) is substituted 
with the immediately preceding agent or clause. If the dummy is language specific 
(e. g. the string 'it') the immediately clause is the substitute. The object dummy (O) is 
substituted with the immediately succeeding clause. 



The fundamental assumption is that the ecological facts are linguistically 
packed in such a way that viewpoints can be discovered, differentiated and integrated. 
By means of an unfolding of the (AaO) formula into a multiple linked ((AaO) a 
(AaO) n ) system, ecologically valid information can be extracted and abstracted. The 

meaning of this intrasystemic analysis only appears in the Kantian schema as 
synthesis. The linkage mechanism of expression (7) illustrates how the schema axiom 
may guide the development of the formula (2) into an algorithmic procedure 
characterized by functional, structural and dynamic aspects. 

Making consciousness the outcome of the cooperative process of the 
constituent components of the Kantian schema implies that the action component (a) is 
the umbilicus, i. e the point of reference for the mechanism. The leading idea of the 
algorithm is that consciousness must be understood in terms of the agent rather than of 
a physical, symbolic or conceptual entity. 

The states of a system of this kind are determined by the mutual dependencies 
(affinities) of its constitutive components. The affinity relations between the coop- 
eratively operating and interacting components create the absolute terms, i.e. the 
invariants, which serve as point of departure for synthesis. The Kantian schema 
implies an interrelation and transformation of analytic concepts resulting in synthetic 
concepts. This process has to be conceived of as a merge of the empirical with the 
formal aspect of the evolving system. 

In behavioural science terms, this means that the phenomenon of 
consciousness must be conceived as the synthesis of an active inquiring agent. The 
agent's ability of self -reference is the fundamental assumption and implies that no 
master interpretation can be forced upon its verbal expression. When self -reference is 
concealed or non-detectable, it deprives us of the possibility of knowing what is 
folded and represented by strings of symbols. Further, if such strings cannot be 
recognized as intentional verbal behaviour, they cannot serve the purpose of carrying 
meaningful information either. 

The overall importance of the Kantian schema as methodological tool and 
conceptual framework for a logic of discovery rests on the assumption that an 
organism, being able to express itself freely, creates information of high validity. This 
means that the strict dependency of the (AaO) formula relates the perceiver with the 
perceived or more generally, the knower with the known. Consequently, self-reference 
need to be incorporated as the integrative component of the schematizing process. 

Language as Carrier of Consciousness 

The Kantian schema as link in a theory of consciousness is as fundamental as 
the axiom of number in a theory of physics. This has consequences for the conception 
of the Space-Time relation. In Kant's transcendental logic it refers not only to the 
relation existing between independent or associatively related substances and 
abstraction but refers to the relational order (affinity) that come into existence by a 
cooperative act. Kant conceives of consciousness as the product of a schematizing 
process. 

Karl von Frisch (1967, Fig. 28-29, 46 and 52) studied "The dance language 
and orientation of bees" within a natural science context (see Fig. 1). Within his 
famous research program, he developed a demonstrative definition of the Kantian 
schema. To speak of schematizing would require the demonstration, that the dance 
patterns of bees carry a definite meaning. This requirement exactly fits the dance pat- 
terns. Frisch's experiments showed that a foraging bee (Fig. 28) performs the "round" 



10 



Figure 1. 

Dance Language of Bees 

From "The dance language and orientation of bees" (pp. 29, 57, 59) by K. Frisch, 
1967, Cambridge, MA: The Belknap Press of Harvard University Press. Copyright 
1967 by Harvard University Press. Reprinted by permission. 




FIGURE 28. A forager (lower left) who 
has returned home and is giving nectar to 
three oilier bees. 




FIGURE 29. The round dance. The dancer 
is followed by three bees who trip alonu 
after her and receive the information. 




l-'KJURli 46. The tail-wagging dance. 
Four followers are receiving the message. 




FIGURE 52. Tail-wagging dance with a 
large number (eight) of followers. In this 
sketch are shown also the nonparticipating 
bees in the vicinity. The movements of the 
darning group clear a little free space on 
the thickly populated comb. The positions 
of the bees are taken from a photograph. 
Feeding station 2000 m distant. 



11 



(Fig. 29) or "tail-wagging" dance (Fig.46) if and only if the foraging is worthwhile. A 
"round" dance clearly indicates that the sources of food are nearby. A "tail-wagging" 
dance is performed when the food sources are at a greater (> 100 m) distance. The 
"tail-wagging" dance, moreover, announces also the direction of the goal by means of 
the axis of the dance relative to the position of the sun (Frisch, 1967, p. 142). In 
addition, the duration (ca 15 sec.) and vigorousness of the dance relate to the amount 
of either nectar or pollen discovered. The better the source the more energetic and 
long-lasting is the dance. 

The reference factors (int (A) and (ort (O)) will now be used with the purpose 
to study the specific process of schematizing. By casting the dance language of the 
bees into the (AaO) formula a radical different procedure for the schematizing of von 
Frisch's results is intended. The formula (3) may be realized through the action 'to ob- 
serve'. The nominalization process is initiated in order to test its abstractions for 
structural affinity and for the self-referential properties of the bee as inquiring agent 
(A). In the present context it is sufficient to assume finite sets of values (= textual 
strings) reflecting the case of nominal or linear variables. Thus expression (6) carries 
the original structural information necessary for the development of a mental 
processing of textural information. During the processing both structure and process 
are modified through successive contribution of novel information. The manifestation 
of the A- and O-components belong to an observation, where the expression becomes: 



Bee 


A 








observe 


a 








that 


(0)<- 


A 


a 









Bee 


dance 


food place 



(8) 



The dummy (O) signals that the object linkage has to be solved through reference to 
the succeeding clause. The dummy (O) symbolizes some observable whose variables 
include an agent and an object involved into an event. In von Frisch's study it is the 
dancing event which contains the ecological significant information that becomes 
available. The dancing bee performs a series of actions. For example, it uses its own 
body to communicate integrated information within a discontinuous Space-Time 
system. Any movement, such as wing-strokes without the intention to fly is a 
ritualized expression by which the bee creates a "language space" for an "analog T" 
(Jaynes 1967, p. 62-66) to transform its awareness of distance to food places into ab- 
stractions. (Note: Consciousness) and to communicate its consciousness to a fellow 
bee. 

By means of a differential analysis von Frisch studied the way in which a bee 
observes another bee as well as the way in which varied colonies of bees intentionally 
communicate their awareness. The fundamental idea behind von Frisch's careful and 
thorough control of intention and orientation is that a symbolic expression has to 
express self-reference. The consequences of this standpoint are that the medium has to 
contain species-specific carriers of information and that the organism has to have a 
device for "lifting the information from its carriers" (Foerster, 1969). Frisch's ambition 
was to measure whether sounds and movements are carriers of specific information. 
As Gibson (1979, p. 42) observes, an organism learns to discriminate within a 
"behavioural loop" what another perceives. With this point of departure, a bee 
observing another bee picks up information about movements from an "ambient optic 
area" (Gibson, 1979, p. 203). The optical pattern available to the observing bee is 
specified by the movements of the dancing bee. Its body generates a particular texture 



12 



flow with its characteristic invariants. In the sense that the ecologically oriented 
geometry of awareness is directly determined by the geometry of texture, an unknown 
objective becomes known for the observing bee through the performance of the 
dancing bee. Thus, it can be argued that the "knowing together", i. e. con-sciousness 
has emerged for participating bees (Fig. 52) while others remain uninformed. 

Making information something that emerges as a result of a cooperative 
process presupposes the possibility of tying the effect of an experience to a related 
activity instead of attributing it to some unrelated mechanism. If one with Gibson 
(1979) may assume that expressive behaviour manifests itself in informative light, this 
implies that the structure of an object or event can be studied through change. But 
"regularities" in change can be sensibly measured only with reference to a particular 
organism. Otherwise an assessment of what is known becomes meaningless. The 
functioning of the Schema in formalizing knowing can now be summarized: 



Bee 


A(l) 


the knower 


(9) 


observes 


a 








Aa(O) 


the known (integrated experience) 




that 








Bee 


A(2) 


the experiencer 




dance 


a 






food place 





the environment 





The relation between the two agents is asymmetrical in the sense that Agent(2) 
is experiencing an unknown environment, while Agent(l) has already integrated this 
kind of experience. Frisch (1967, p. 43) observed: "Those that have been collecting 
from the same kind of flower often give attention to one of their fellows from a 
distance of as much as 2-3 cm hasten to her." The experiencer-environment relation is 
known to her. Consequently, in his observations the knower is always present in the 
known. Whenever a knower intuitively knows the unity, it appears as one whole. In 
this sense, Kant has given a precise definition of intuition in his concept of Schema 
(Bierschenk, 1981, p. 14). Because the relationship between dance and food place are 
maintained as a result of Kant's transcendental logic, the topological structure of the 
ambient visual area transcend both physical and mental realities in which the 
relationship become realized. 

Further evidence for this interpretation comes from the study of Regan, 
Beverly and Cynader (1979). The results of their experiments with a psychophysical 
model of stereoscopic motion indicate that ecological invariants exist in the visual- 
flow pattern. The authors have demonstrated that a variation in object orientation is 
important for the organism in its pick up of "exterospecific information". After this 
kind of information has been picked up from its carriers, the organism can extract the 
ecological invariants and needs not rely on concrete matter or energy. Moreover, a 
symbolic expression of self-reference allows for the detection of "propriospecific in- 
formation". By anchoring knowing in these two poles, knowing the world prerequires 
the extraction of invariants from expressions of mediating experience. 

Detection of Ecological Invariants 

The ability to pick up information can be measured by covarying organism 
and environment. Since the variation in perspective is supposed to be dependent on an 
inquiring agent, it is tempting to study the degree to which this ability is inborn. 



13 



Symmetrically expanding shadows specify an approaching object within the 
ambient optic area. This fact were used by Ball & Tronick (1971) to test whether a 
newborn infant of only a few weeks of age detects quality of direction and relative 
depth. An infant sitting in a chair in front of an experimental arrangement was 
exposed to real objects and shadows on symmetrical and asymmetrical paths towards 
the infant's face. By simulating variations in perspective through real and virtual 
objects on the mispath they could make explicit that an inborn mechanism for per- 
ceptual information processing exists. The infant's avoidance behaviour implied that 
this mechanism works with high precision and high sensitivity concerning the direc- 
tion of motion and the distance of the moving object. 

The meaning of the event, in this case the object approaching the "centre of the 
ego", seemed to be immediately perceived as "danger for life". Thus, schematization 
implies not only information processing but also prospective reference to a future 
event, provided it is threatening enough for the survival of the organism. This con- 
clusion is worth a thorough analysis by means of the (AaO) formula: 

(10) 



The researchers 


A(l) 


observe 


a 


Aa(O) 





that 




the infant 


A(2) 


discriminates 


a 


paths 






As in the case of the bees, the dummy symbolizes the environmental variable. 
In the actual case, it is an event which incorporates an agent and an object on a path. 
From an ecological point of view the expression (10) manifests the fact that perception 
of the environment is an activity that twins together the perceiver and the perceived in 
a cooperative relation, without which the meaning of the perceived cannot be 
established. 

The significance of the asymmetrical relation between the two agents lies 
partly in the manipulation of the object orientation of A(2), which makes available 
exterospecific information, partly in the manipulation of A(2) perspective, which 
allows some inferences about the abstraction of propriospecific information. The 
result is the observation that an infant of only a few weeks of age acts on the basis of a 
highly selective perceptual Schema. Lorenz (1950) and Tinbergen (1951) call this 
same mechanism a Schema in the Kantian sense. But there is neither evidence of a 
basic structure of language nor of consciousness. In the absence of communication, 
the meaning of the object is still dependent on correctly drawn inferences based on the 
geometry of motion. 

The Intentional Use of Ecological Invariants 

The experimental structure embedded in the design described by formula (2) 
will be studied further by applying a generalization of the expression (2) on the 
behavioural discrimination of contours: 

(*(A))a and a(*(0)), where * indicates intentions and orientations respectively (11) 



14 



The expression (11) constitutes the basis for transfiguration. By twisting and 
manipulating the measuring variables "Organism" and "Environment" of the Frisch's 
study it becomes possible to give a formal expression to the cooperation of both: 

(org(A)a) and (a(env(0))) (12) 

The organism-environment interactions captured by Gibson and Walk (1960, p. 65) 
and the environmental structure embedded in their 'Visual Cliff design (Fig. 2) will be 
made explicit with expression (12) as instrument. The process anticipated to operate in 
this structure is dependent on the values (-,+) assigned to the action (a). With or- 
ganism and environment as experimental factors a new set of four variables becomes 
available: 

(1) A fixation of both (A- 0-) represents the event depicted by the top left 
picture: A child of crawling age is introduced in order to specify the agents place in 
the environment, i. e. the centre board. Fixating both implies that neither the variation 
in the viewpoints nor the variations in the shifts of perspective can be measured. This 
is essentially the zero hypothesis of perception. A stationary environment is sensed by 
a stationary organism. Many procedures have been developed to create this state with 
the purpose to calculate the power of sensory stimulation. Stimulation above a certain 
value causes a response in the organism, so that the environmental information can be 
sensorily processed. But this does not imply perception. 

(2) First through a manipulation of the environment by mobilizing the O 
component (A- 0+) variation in viewpoints are introduced and consequently, 
exterospecific information becomes available. This implies that an object orientation 
is initiated. At least two viewpoints although of different kind are observable. These 
are the checker squares of the surface texture and a lure in the form of the mother. The 
minus sign tied to the A component signals that no variation in perspective is implied. 
Contrasting of viewpoints of the same type is required. The result is 

made visible by the top right picture: The child crawls to its mother across the 
"shallow side" of the cliff. 

(3) By mobilizing the A component (A+ 0-) it is presumed that the Agent's 
perspective varies, i. e. it gets a different angle of inclination. This implies a shift in 
perspective. A state change is the result and documented by the body-floor relation in 
the bottom left picture: The child has turned around its body and tests the solidity of 
the glass surface by patting it at the "deep side" of the cliff. 

(4) The complementary relationship between the variations in exteroception 
and proprioception can be observed by mobilizing both components (A+ 0+). This 
implies that the affordance of the cliff can be detected. The result is pictured at the 
bottom right. The mother calls the child from the "deep side" of the cliff. The child 
has the deep side in front of it. 



15 



Figure 2. 

The Child's Depth Perception 

From "The 'Visual Cliff" by E. J. Gibson, R. D. Walk, 1960. Scientific American, 
202, p. 65. Copyright 1960 by Scientific American, W. H. . Freeman and Company. 
Reprinted by permission. 





16 



The Visual Cliff experiment has been set up primarily for studying: 

(1) the detection of tranformational invariants, which specify the nature 
of change, and 

(2) the detection of structural invariants, which specify the identity of 
the structure that undergoes change. 

Gibson, Kaplan, Reynolds and Wheeler (1969) have argued that humans can directly 
perceive going or coming out of view as opposed to going or coming out of existence. 
Their argument has further consequences, namely, (1) any point in the environment is 
a possible point of observation, and (2) the organism's perceptual mechanism analyzes 
what is "offered" to it, i. e. what comes into view. Since such an analysis is 
fundamental for the survival of the species, the organism or individual makes 
intentional use of the information. It is therefore assumed that "egomotion" is 
encompassed in perception. 

Because the ecological approach to visual awareness required an experimental 
setting in which perception of what is offered could be tested behaviourally, it was 
necessary to find a method for measuring optical information processing. The problem 
was solved in such a way that Eleanor Gibson's behavioural interest was built into the 
perceptual design carrying the ecological invariant. It was assumed that fear of hight is 
the negative emotional reaction that most significantly shows the intention of survival 
among the species. Consequently, the behavioural study of the sensitivity to hight was 
made the key for inferring meaningful behaviour toward the Cliff as a natural clue to 
danger. 

In the picture series it is demonstrated that a cooperation of the organism with its 
environment requires locomotion. As the pictures document, the infant is required to 
locomote (by crawling) and to orient itself across the Visual Cliff. This task could be 
performed by the researchers placing a lure, such as the child's mother, at the other 
side of the arrangement. If the infant refuses to crawl over the deep side, this is taken 
as evidence of fear of hight and depth perception is concluded. Moreover, it is 
demonstrated that awareness of an edge is a function of changes in both perspective 
and viewpoints. Changes in the infant's perspective increase with increasing locomo- 
tion. The ability of abstracting transformational invariance is thus a function of this 
locomotion and the differentiation of the objectives. The general result of the Visual 
Cliff experiments will now be presented with reference to expression (6): 

(13) 



The researchers 


A(l) 


observed 


a 


Aa(O) 





that 




the infants 


A(2) 


avoid 


a 


the deep side 






Schematization synthesizes and preserves the origin of a developmental process. 
Therefore, progression implies a behavioural development in which every new phase 
is characterized by distinctive aspects. These increase the organism's autonomy in 
relation to its environment, and thus it chance to survive. At this stage in development, 
novel differentiations and integrations change the characterizing function of the 
Schema manifested in a corresponding change in the nature of information. The 



17 



observed regularities in the infant's behaviour make possible an inference about an 
observed fact, namely avoidance behaviour as indication of a "negative affordance". 
But consciousness cannot be measured by this design. The meaning of the cliff has to 
be communicated by means of a text that captures the affordance of the experimental 
set-up. 

Textual Transformation 

Tinbergen (1951) showed by means of contour coding experiments that the 
structural transformation of a surface is necessary if it shall carry information that the 
individual of a certain species can use. Independent of its position on the evolutionary 
scale, it does not simply react to external influences. It selects, transforms and orga- 
nizes information. This observation implies that a pictorial or graphical display has to 
depict crucial structural qualities in such a way that the individual can capture its 
significance by extracting higher order functions, which are assumed to be shapeless, 
formless and transcendental. "Direct perception" does, according to Gibson, extract 
and abstract the ecological significant invariants of the surrounding world. Of 
fundamental importance in the individual's perception of its environment is the 
affordance of an object or event. Affordances are defined as "invariant combinations 
of properties at the ecological level" (Gibson, 1979, pp. 127-140). 

What can be observed in the experiments presented thus far is a systemic 
thinking, in which the (AaO) formula has governed the layout of the experiments. It is 
due to Lorenz's (1941) transformation of the Kantian schema into a natural science 
context that the Schema as hypothesis has become attractive in psychobiological 
research. Sperry (1952) for example developed his theory of "chemoaffinity", which 
established the basis for his split-brain experiments. As a result, Sperry (1969, p. 533) 
comes to the conclusion that "consciousness is an integral part of the brain process 
itself and an essential constituent of the action". 

By applying the (AaO) formula to the analysis of behavioural outcomes it was 
possible to show that the synthetic proposition is the necessary instrument for the es- 
tablishment of consciousness and that consciousness is closely tied to a linguistic 
mechanism. The essential key concepts for establishing conceptual invariance are 
"perspective" and "viewpoint". 

For a conceptual coding of language the empirical context has to be known and 
the Agent function (perspective) be determined. Perspective control lies in the 
definition of a agent, which in turn, determines what viewpoints are chosen and how 
they change throughout a text. It is assumed that a pictorial and symbolic expression 
of the organism-environment interaction entwines perspective and viewpoints in the 
same way as intention and orientation have entwined organism and environment at the 
preceding level of behavioural analysis. It follows that the experimenters' 
consciousness of the organizational layout of the cliff must be studied by applying the 
(AaO) formula to the Caption text of the picture series namely: 

"CHILD'S DEPTH PERCEPTION is tested on the Visual Cliff. The apparatus consists 
of a board laid across a sheet of heavy glass, with a patterned material directly beneath 
the glass on one side and several feet below it on the other. Placed on the centre board 
(top left), the child crawls to its mother across 'the shallow' side (top right). Called 
from the 'deep' side, he pats the glass (bottom left), but despite this tactual evidence 
that the 'cliff is in fact a solid surface, he refuses to cross over to the mother (bottom 
right)." 



18 



The Caption text produced by the researchers is an expression of their degree of 
consciousness which becomes materialized through the textual flow. But 
transformations in the text are of a multivariate kind and therefore far too complex to 
be comprehended without a topological analysis and topographical representation. 

Algorithmic Text Processing 

Whenever observational events structure the language of an observer, this 
language contains information belonging to these events. Events are basically, the 
discontinuities in the textual flow. When it comes to present observations as a series, 
this is continuously done in the form of a process linearizing the phenomenon to be 
expressed. Thus the observations are given a syntactically coherent form. 

The developed algorithm takes the production of natural language in the form 
of speech or text as an expression of an Agent's (A) cooperation (a) with some 
environment (O) with the aim of finding its absolutely simple constituents and its 
mechanism of transference. A strict dependency between these constituents creates the 
synthetic concepts. In the moment of text production, an observation is put into 
perspective. The experience of the Agent builds on actions implying that intention and 
orientation are incorporated into the perspective underlying the verbal flow. The 
perspective is defined through two points. One is the point of observation and the 
other the point of view, e. g., the horizon. Within these boundaries, processing of 
information comprises variable measurement of viewpoints which are focused to 
varying degrees of perspective inclination. The textual expression of the degree of 
variation is the distance between the point of departure (= beginning of running text) 
and the folded and serially ordered viewpoints of the text. There is a general 
topological correspondence between the events and the information presented through 
language. While maintaining its topological coherence, the nature of the information 
contained in a particular text changes as the process of textual production progresses 
from one terminal state to the next. 

The graphical reproduction of an observer's perspectivation is essentially a 
pattern of strings of symbols and spaces in between, demarcated by a point at the 
beginning and end of each pattern. Note: That these strings carry the symbolic 
information commonly associated with words is of no relevance in a systemic 
determination of information. On the other hand language has to contain specific 
information that can be picked up from these carriers. In expression (16) the algo- 
rithmic functioning and the lexical notions of some sentence markers are shown. 

The algorithm also has to work with clause openers which have the function of 
demarcating the boundaries of a clause except for the end of running text. Clause 
openers may be word grapheme as well as junctional graphemes. A graphical clause is 
part of a sentence. As illustrated in expression (16) a clause opener succeeded by 
another one defines the boundary as the end of a sentence in the technical sense. Thus, 
any first clause opener of a series is redefined as sentence marker. By this measure, 
the algorithm brings out implicit sentence markers. The algorithm defines on purely 
formal grounds the organizational frame of a sentence. But this frame is insufficient 
for processing the perspective in the verbal flow. What is required for a final analysis 
is a structural approach. 

The Schema marks the structural aspect of a string of symbols. Schematizing 
incorporates the assumption that higher order functions are underlying the verbal flow, 
though not directly apparent from the analysis of syntactic categories. In the 
generative process, the analysis starts on the basis of the component represented by the 
verb. Without the identification of a verb, it is impossible for the algorithm to disclose 



19 



a mental process. If the algorithm identifies two or more verbs, this will result in a re- 
cursive cyclic processing as many times as there are verbs. A procedure keeps track of 
the number of verbs within a particular clause and inserts immediately before any of 
two verbs the technical clause opener (that). 

The verb 

As verbs are recognized all finite and inflected verbal forms and participles 
inflected in concord with the grammatical subject. The following form categories 
related to the Visual Cliff Caption may be illustrative: 

(15) 



Form Category 


Visual Cliff Examples 


imperative 


test 


present tense 


consists, pats, crawls, refuses 


preterite indicative 


patterned, placed 


preterite conjunctive sat 




infinite 


to cross 


present participle 


crossing 


perfect participle 


laid, called 


supine 


looked 



The definition is based on the assumption that the verb as predicative category 
and word class has to carry the controlling function in the final decision as to whether 
a clause is present or not. A consequence of this definition is that in Swedish language 
the particle-verb compounds and reflexives are not included, except the passive 's'. 
This implies that deponent verbs are considered to be part of the passive construction 
expressing an unknown Agent. Furthermore, the definition circumvents all problems 
associated with auxiliary verbs. Such verbs are treated as autonomous verb forms, that 
cause the algorithm to initiate a recursive cycle whenever an auxiliary and a main verb 
coincide. From a structural point of view, it has turned out to be an advantage to treat 
the auxiliary verbs as basic verbs. Basic verbs such as 'shall' and 'have' seem to be 
associated with fundamental life conditions (Jaynes, 1976, p. 51) and are for action as 
imperative as 'go' and 'stop' are for a mechanically functioning system. 

At some stages of development, human perspective was very shallow and only 
could absorb a language based frame of action (I. Bierschenk, 1989). It is worth 
noting that a few basic verbs are immediately accessible in critical situations under 
time pressure, or when freedom of action is constraint and choice of strategy unclear 
(Bierschenk & Bierschenk, 1986). Moreover, the indicated algorithmic use of basic 
verbs results in clarity and precision of the analysis process. Finally, the copula 'is' has 
traditionally the task to connect a main word with an attribute in a symmetrical 
relation. The algorithm recognizes 'is' in the same way as any other verb in a directed, 
i. e. asymmetrical relation. 

The algorithm has been operationalized by Helmersson (1987, 1991) in the form 
of a computer program which takes its departure in natural produced text. The details 
of the algorithmic processing and the approximately 50 rules of the system have been 
presented in Bierschenk and Bierschenk (1986). Consequently, the Caption text to the 
picture series has been subjected to the following procedure: 



20 



(1) (AaO) encoding 

(2) Supplementation of A- and O-dummies 

(3) Generation of A/O matrices 

(4) Cluster analysis 

(5) Topological analysis and topographical representation. 



The procedure has led to the following outcome, for substitution of A-dummies 
(A)aO and O-dummies Aa(O) see (7): 

(16) 



Block 



Code 



Block 



Code 



Block 



Code 



Block 



Code 



(.) 


00 


with 


70 


(top 


60 


j 


0100 


01 (that) 


01 


a 


70 


left) 


60 


09 but 


01 


(A)aO 


30 


Aa(O) 


70 


06, 


01 


despite 


30 


Child's 


50 


04 that) 


01 


the 


30 


this 


30 


depth 


50 


(A)aO 


30 


child 


30 


tactual 


30 


perceptior 


i 50 


patterned 


40p 


crawls 


40 


evidence 30 


is 


40p 


material 


50 


to 


60 


that 


0130 


tested 


40p 


directly 


50 


its 


60 


the 


30 


on 


60 


beneath 


60 


mother 


60 


cliff 


30 


the 


60 


the 


60 


across 


60 


is 


40a 


visual 


60 


glass 


60 


the 


60 


in 


60 


cliff 


60 


on 


60 


shallow 


60 


fact 


60 


. 


00 


one 


60 


side 


60 


a 


60 


02 (that) 


01 


side 


60 


(top 


60 


solid 


60 


The 


30 


and 0160 


right) 


60 


surface 


60 


apparatus 


30 


several 


60 


a 


00 


10, 


01 


consists 


40a 


feet 


60 


07 (that) 


01 


he 


30 


of 


60 


below 


60 


(A)aO 


30 


refuses 


40a 


a 


60 


it 


60 


Called 


40p 


Aa(O) 


50 


board 


60 


on 


60 


from 


60 


11 to 


01 


03 (that) 


01 


the 


60 


the 


60 


(A)aO 


30 


(A)aO 


30 


other 


60 


'deep' 


60 


cross 


40a 


laid 


40p 


. 


00 


side 


60 


over 


60 


across 


60 


05 (that) 


01 


08, 


01 


to 


60 


a 


60 


(A)aO 


30 


he 


30 


the 


60 


sheet 


60 


placed 


40p 


pats 


40a 


mother 


60 


of 


60 


on 


60 


the 


50 


(bottom 


60 


heavy 


60 


the 


60 


glass 


50 


right) 


60 


glass 


60 


centre 


60 


(bottom 


50 


. 


0090 


0160 


board 


60 


left) 


50 







In the case of a passive voice expression (p) the dummy (A)aO is 
supplemented with the a priori defined Agent (X) which is always activated. This may 
be exemplified by the first block of the Caption to the picture series which contains 
the passive voice as cue to the Agent. The two-figure code system carries the 
complementary dimensions intention (first figure) and orientation (second figure) 
according to the following scheme: 



21 



Component Code Component Code (17) 



Sentence opener 


00 


Figure 


50 


Clause opener 


01 


Ground 


60 


Context 


10 


Means 


70 


Experience 


20 


Setpoint 


80 


Agent 


30 


End of text 


90 


Action 


40 







The scope of action 

Conceptual components require a systemic arrangement of the (AaO) relations 
such that intentionality and directiveness can manifest themselves through linguistic 
variables. Linguistic variables may get different functions depending on perspective. 
Syntactic cues to conceptual description are the prepositions, which functions as point- 
ers to the viewpoints of the subcomponents of the Objective (50, 60, 70, 80). Thus, the 
scope of action is precisely defined by number and kind of the prepositions. The scope 
of action and prepositions may be exemplified by some verbs from the Visual Cliff 
Caption: 

A .a O Code (18) 



X 


is tested 


without prep. 


50 


The apparatus 


consists 


of 


60 


X 


laid 


with 


70 



The component assigned help to illustrate their positional change and, as already 
indicated, change of function is an expression of perspective. The conceptualizations 
depicted in expression (18) follow closely a pure linguistic approach. But all 
viewpoints involved in every action are lifted up onto the observational level in case 
they have been left out by the observer. To be complete each observation must express 
an (AaO). On the observational level, however, this relation does not always get its 
manifestation in language. With the help of context the observer may chose not to 
make explicit the full relationship and still be understood. On the other hand, the 
scope is decided upon by the empirical context and has sometimes to be supplemented 
into the verbal expression for making its algorithmic processing possible. The al- 
gorithmic processing of an observation only can be carried out if the complete 
conceptualization of the observation is made explicit. This explicitness has to be 
obtained with reference to the scope of action and the empirical context. 

Applied to the observations on the Visual Cliff, it denotes the determination of 
the point of departure, i. e. the Agent (X). The perspective of an observation may be 
wide. In this case it addresses the actions of both the observer and the observed. A 
narrow scope encompasses only the event on the cliff. Which scope is to hand can 
only be decided upon, if and only if the Agent is under control (I. Bierschenk 1987), 
because it has the steering and control function. It follows that the Agent must always 
be unequivocally identifiable, if any action shall be processed. 

Supplementation 

When the Agent is covert syntactic cues need to be employed to identify the 
Agent. Consequently, supplementation is strongly connected to the definition of the 
scope of action. The textual description of the Visual Cliff is done on the assumption 



22 



that the experimenters govern the scope of action. They have set up the device and 
staged the observations. The analysis of the steering function of the Agent has been 
worked out by I. Bierschenk (1987) on the basis of the sample text: 'I should observe 
infants.' The difference between a positional (S v O) and a perspective (AaO) 
approach is exemplified: 



String 


Control 






(SvO) 


(AaO) 


(•) 




00 


Why 


^adv 


01 


(A)aO 




30 (X) 


should 


v 


40 


I 


S 


50 


(that) 




01 


(A)aO 




30 (X) 


observe 


V 


40 


infants 





50 


C) 




0090 



(19) 



I. Bierschenk (1987) observes: "The obligatory insertion of the Agent that is made by 
perspective analysis does not imply a complementary addition of a surface structure." 
The example shows that classical linguistic analysis is position bound, but it is not a 
question of filling a position. The challenge lies in taking the question marker as 
signal for initiating transformational processes. The (X) is the controller of the point 
of reference of what is being said of "I" It follows that "I" can be discovered as a 
viewpoint. 

Intentionality and orientation 

Both concepts imply a need for the indication of direction. This is achieved 
through the distinction of the Agent as centre or starting-point of an action from its 
viewpoints. The verb string is the umbilicus for the processing and must be identified 
by means of a supplied dictionary. The mechanism executes its work by searching for 
the viewpoints marking the orientation. Any string following immediately after an 
active verb is a materialization of one or more concrete or abstract viewpoints. The 
complementary move is carried out to mark any string preceding an active verb as the 
manifestation of the textual agent or agency in the expression. In the passive case, the 
Agent is marked with the variable X. 

The Objective Component 

The differentiation of the Objective component within a perspective clause is 
made on the basis of prepositions. In principle, this concerns the prepositions 'on', 
'with', and 'for'. These have the function of representing three kinds of pointers toward 
structural variability. The perspective order between them is the presented one and 
refers to the distance from the verb. Viewpoints that are not preceded by a preposition 
are next to the verb and in direct focus. The preposition 'for' points toward something 
very distant beyond the visual field, i. e. toward the setpoint. With respect to the 
algorithmic approach, 'for' has priority over the other two and 'with' has priority over 
'on'. This principle governs the relative position of the viewpoints. But perspective 



23 



differentiation is possible only within the Objective component. If prepositions appear 
in the Agent component, they are treated as integrated in the Agent variable. 

Figure and Ground. Both are subcomponents of the Objective component: 
The Figure component denotes the absolute point of reference. This circumstance is 
syntactically identified through the absence of prepositions. A text consists of a 
number of perceived or conceived viewpoints presented in a certain determined order. 
A particular observation may refer to the immaterial existence of an event (e. g. 'depth 
perception') toward which the action is directed (Block 1). 

The Ground component represents the absolute axis of reference and marks distance as 
an extension along the ground. In principle, the component does not rely on the 
abstract notions of Space and Time. Instead, the axis is empirically based and comes 
into existence through the Agent's cooperation with and exploration on the floor. In 
principle this concerns a spatial orientation which is syntactically identified by 
prepositions of the following type: 'in', 'on, 'under'. The operating strategies 'on the 
Visual Cliff have all their viewpoints linguistically expressed. 

Means and Setpoint. Both are optional subcomponents of the objective 
component: 

The Means component. When a means is present it is regarded as an explication of the 
action which, however, does not effect its scope, but the number of viewpoints in the 
observation. A means gives expression to an optional aid or instrument by which the 
action is performed. Syntactically, the viewpoints associated with the Means com- 
ponent are identified by the prepositions 'with', 'through' and 'by'. In the Caption to the 
picture series only one instance is present (Block 3). The concrete action of the agent 
(X) is directed toward the glass in order to give 'one side' the appearance of substance. 
Setpoint. What can be perceived or conceived beyond the limiting horizon of the ex- 
perimental environment has not been realized in the Caption. This means that the ex- 
perimenter's intention with the experimental arrangement is implicit. Syntactically, the 
viewpoints associated with the Setpoint component are identified with the preposition 
'for'. From the perspective of the experimenter, the picture series has been composed 
with the intention to represent the simulation of the experience of falling for a child. 
This intention lies beyond the horizon of the experiment. The absence of this 
subcomponent indicates that the idea of the experiment has not been expressed ver- 
bally. The reason may be that the experimental description is well anchored in the 
design. Consequently, an explanation of intention beyond the experimental frame 
seemed superfluous. However, a present Setpoint does not denote the fulfilment of the 
intention. 

Concentration of the Viewpoints 

In general, the algorithm identifies four different kinds of viewpoints. It is 
capable of transference and functional redefinition of Agents and Objectives as illus- 
trated by the Blocks 4 and 8. The results of this processing will now be presented in a 
blockwise fashion: 



24 



30: X (20) 

50: CHILD'S DEPTH PERCEPTION 
60: on the visual cliff 

30: The apparatus 
60: of a board 

30: X 

60: across a sheet of heavy glass 

70: with X+material directly beneath the glass 

30: X 

50: material directly 

60: beneath the glass on one side and several feet below 
it on the other 

30: X 

60: on the centre board (top left) 

30: the child 

60: to its mother across the 'shallow' side (top right) 

30: X 

60: from the 'deep' side 

30: he 

50: the glass (bottom left) 

30: despite this tactual evidence that the 'cliff 
60: in fact a solid surface 

30: he 

50: he+over to the mother (bottom right) 

30: he 

60: over to the mother (bottom right) 

It is essential to realize at this point that the developed algorithm is based on 
observable properties of the Caption text being recognized. Block 1 illustrates that the 
intention and orientation of the text producers is integrated into the verbal description. 
The block (1) incorporates the assumption that the ecological significant information 
embedded in the textual structure becomes accessible only in relation to the activated 
variables (30, 50, 60). The crucial novelty of the algorithmic processing lies in the 
manner in which the variables apply to the text. They are named variables, because 
they interrelate the behavioural or qualitative character of any text. By means of the 
variables it is possible to perceive directly the variability of textual behaviour on the 
phenomenological level, but this variability is only virtually identical with the vari- 
ability of the underlying textual flow. 

Variables are not to be understood as names referring to something. The 
decisive step is the transition from Agent or Objective as constituents of a system 



25 



comprising the object of study to agents or objectives as variables of the system to be 
observed. The block (1) gives expression to the intention carried by an unknown 
agent. Consequently, the agent as variable takes the string (X) as its value. The 
information of the viewpoints of the block (1) is carried by the variable codes for 
figure and ground (50, 60) expressing imagination and orientation. Thus, a variable of 
the system is some characteristic which, in principle, can be measured directly. The 
Caption begins with 'Child's depth perception' which is a specification of the state of 
the system at a particular point in time. Algorithmic processing implies that the string 
is taken as the 'value' of the variable (code 50). It is the code of the Figure component 
and marks the absolute point of reference. The algorithmic coding procedure does not 
instantiate some logical definition of the variable, but provides a starting point for 
observation and measurement. Here, the orientation is toward something more abstract 
than the environment itself. Intention is something inherent in the Agent which gets 
expression through the Figure. What is expressed is more abstract and more integrated 
information compared to the information carried by the Ground component. This is 
easily seen by the textual string of the Ground component: 'on the Visual Cliff. The 
syntactic cue to the Ground is the preposition 'on'. In the Caption, the instances mani- 
festing the Ground are numerous and concrete. This is due to the fact that the Ground 
represents the instrument of the explanation of the experimental cause. The 
importance of the algorithmic procedure lies in its capacity to evaluate a variable on a 
state of the system which eventually will result in the measurement and representation 
of its dynamics and structure. 

Matching 

Abstracting structural and organizational aspects of natural text implies that all 
strings are processed and tested for their distinctiveness. This process is initiated by a 
routine that tests the completeness of a block. During the coding process a block is 
procedurally defined whenever a 01 -code precedes and succeeds some textual strings 
which include a verb string together with a string taken as value of the variables (code 
30, 40, 50/ 60/ 70/ 80). When all codes are adequately represented all strings are 
further processed by a routine that generates unique strings. The comparison of strings 
depends only on intrastring criteria. 

Unique strings are the basis for setting up a series of binary matrices of the 
(Nxp) type, where (N) represents the textual agents and (p) represents the textual 
viewpoints (v.). The function of the agents is to guarantee the coordinative structuring. 

Thus, the agent as variable is the makeshift instrument for change of position and 
transference. Its logical content is nothing else but a point in a pattern of relations 
produced by the matrix generation process. 

Table 1. 

Matrix k,: Viewpoints of the Figure Component 

12 3 4 1. Child's depth perception 

2. Material directly 

X 110 3. the glass (bottom left). 

He 11 4. He+over to the mother (bottom right) 



26 



With reference to the Caption text all matrix elements (a--, ) are initially assigned the 

value zero (0). Thereafter, the matrix generation routine marks all relational affinities 
between the A's and O's with the value one (1). The blockwise unique string 
combinations are registered by the following matrices: 

ky 30/50 k 2 : 50/30 k 3 : 30/60 k 4 : 60/30 

1100 10 101110100 10000 

0011 10 010000000 01000 

01 000001000 10000 

01 000000010 10000 

000000001 10000 

00100 
10000 
00010 
00001 

Basically, the textual transformations are conceived of as a series of equivalent 
relations to be established by some linkage procedure. The resulting state variables 
would then establish the link between the original text and the prototypical naming of 
the groupings of the viewpoints. In general, a binary matrix and its transpose represent 
different kinds of agent-related viewpoints. Concentrating the viewpoints means a 
division of the viewpoints of a particular matrix into natural groups. This implies that 
the distance between one viewpoint (v.) and another (v.) in the specified matrix is 

expressed as the distance of these two viewpoints only. 

Dynamics and Linkage 

The dynamics of a text gives expression to the intention of its producer. 
Dynamics generates, modifies or breaks the linkage relations existing between the 
variables established through expression (7). Textual dynamics defines also the 
constraints operating in a text. Such constraints can always be expressed in the form of 
linkage relations. 

Single linkage as a method for grouping of units was developed by Sneath 
(Sneath & Sokal, 1963). His method builds on the simplest procedure of all the 
agglomerative methods developed for estimating the losses of information in the 
attempt of finding natural groupings and structural relations in a set of data. Single 
linkage is defined by the shortest link existing between two units or variables. Other 
linkage procedures are "complete linkage", "average linkage within the group to be 
formed", and "average linkage between agglomerated groups" (Anderberg, 1973, pp. 
137-140). A method which comprises all three procedures has been developed by 
Ward (1963). Ward's goal was to find an agglomerative procedure which could 
minimize the degree of disturbance during the process of agglomeration. His method 
is based on the following fundamental ANOVA equation: 

T = W + B (21) 

where T is the total dispersion matrix, W is the matrix of 'within' groups dispersion 
and B is the 'between' groups dispersion. For any given set of data the matrix T is 
fixed. This means that T is a constant and thus independent of the chosen partitioning 



27 



of a given sample. The grouping criterion, therefore, depends on the functions of W 
andB. 

The first and most important decision concerns the choice of a suitable 
measurement procedure. When observations are independent of size the computation 
of a distance value seems to be the most meaningful procedure for grouping a set of 
measuring objects into natural groups (Sokal & Sneath, 1963, p. 156). Distance as the 
measure has been applied, because the a--, element gives expression to the presence or 

absence (1,0) of an affinity relation. Ward's grouping procedure is based on the 
calculation of an objective function that minimizes 'within group variance' (W). The 
W function builds on the calculation of Euclidean distance which is a special case of 
the Minkowski metrics. A relocation of an individual element of a group is achieved 
by an updating procedure that saves the squared Euclidean distances between group 
centroids. The procedure starts with the total set and defines each element as its own 
group. The one-element group has as its consequence that the Error Sum of Squares 
(ESS): 

ESS = Sum x? - 1/n (Sum x { ) 2 (22) 

where x. is the distance score of the ith element, equals zero (.000). 

ESS = .000 is due to the fact that the numerator equals the squared sum of all 
elements in the group and that the denominator equals the number of observations in 
the group (Ward, 1963, p. 237; Anderberg, 1973, p. 143). At each step Ward's 
procedure considers all possible unions of pairs of groups. The two groups are fused 
that result in the minimum rise of ESS. Initially, the move of an observation from one 
group to another depends on the move of only one border at every iteration and thus, 
effects only a rise in B. By this measure ESS becomes proportional to the squared 
Euclidean distance between the centroids for the agglomerated groups. The recurrence 
formula for the calculation of the distance measure between groups can be found in 
Everitt (1974, p. 17) and is also available in Wishart's (1982) CLUSTAN program. 
Finally, Ward's method differs from common centroid methods in that the procedure 
weights the distance between the centroids during its calculation of the distances. The 
solution of the grouping results in a hierarchical organization of bifurcations. 

The process of concentrating the viewpoints associated with the Figure 
component was carried out with Wishart's program and builds on the amalgamation of 
four textual strings according to the following tree information from the computer 
output: 

Cycle I J Coeff. Items grouped 

12 3 4 

I I I I 

1 12 0.000 - | | 

I I I 

2 3 4 0.000 | 

I I 

3 14 2.000 

Mean = 0.667 Predicted Clusters = 2 
Dev. = 1.155 Realised Deviates =1.15 

(t .80 < 1 ' 63 < t.^ 



28 



Many hierarchic grouping procedure produces dendrogram data. These can be 
represented in the form of a tree. It is easily constructed on the basis of the presented 
tree-data. But these data as well as other relevant information is usually too extensive 
to be reproduced. However, in the actual analysis this information about the groupings 
can be reproduced together with the values of the t-distributions and their confidence 
intervals. The rule used is the "Upper Tail Rule", which is reported in Wishart (1982, 
pp 14-16). The t-statistics with (K = Cluster - 1) number of degrees of freedom is 
computed by a multiplication of the deviates with the square root of (K). Wishart uses 
square root of(n) where n = number of values on the optimizing function, i. e. the 
number of ESS values, which are three in the present case. A K-based instead of a n- 
based test value minimizes the problem of non-normality of the Error Sum of Squares. 
Except for statistical significance, when ever possible the Dendrogram may be ex- 
amined for a natural shred in the hierarchy, which is a classical procedure in all multi- 
variate analysis (Cattell, 1966). Thus the empirical definition of a group founded on 
the Caption text is based on the premise that an obvious break is identifiable such that 
the resulting collinear groups can be given a meaningful name. Moreover, the sig- 
nificance criterion P(t>T) for the t-test has a value of >.20. 

Naming 

The process of concentrating the viewpoints into groups starts from an 
agglomeration of the four textual strings represented in Table 1. Its cluster analytic 
treatment shows that the v,, ~\ and v,,, *, are closest to each other. The prototypical 

naming of these groups abstracts the experience and imagination from the set of 
strings of symbols conglomerated within the respective group. This grouping may not 
immediately be comprehended. One may reason that v,, .. would be closer. Though, 

the manifested relations are the result of the researchers operations, namely testing 
depth perception by preparing the glass surface on one hand and the child's 
behavioural objectives, namely exploring the glass on the other hand. The two el- 
ements linked to the respective group reflect an immediate connection to the upper 
and lower part of the picture series. The upper part represents the object of study, 
namely the experimentally modified floor (strings 1,2). The lower part depicts the 
phenomenon, the scientific focus, which is elucidated through the child acting toward 
the specified objects (strings 3,4). The elements in the groups cohere with Gibson's 
(1979, pp. 156-158) theory of affordance. Naming the two aspects (1) 'The Glass 
Floor' and (2) "The Danger' respectively, reflects the theme of the Caption. 

The process of abstraction and naming has generated analytical concepts 
originating from argumentation about the subject matter. The process of categorizing 
(from Greek kata-, against + agorein = to speak public, from agora = assembly) the 
Caption text has resulted in variables with practically no deviation in import. 
Crystallizing the strings representing the viewpoints, means that a minimally sufficient 
number of groups can be determined. The groups represent analytical concepts which 
have to be understood as an integration of the viewpoints. The result of the integration 
process is indicated by the prototypical names given to the clusters. It follows, naming 
the concepts is synonymous with naming the variables that represent the terminal 
states of the system. With an experimental orientation, it can be argued that the vari- 
ables determine the conditions which allow the abstractions to substitute the original 
text. 



29 



Coordinative Structuring 

The development of a network is dependent on the observed discontinuities 
which are the only reliable observations in the analysis of language as a dynamic 
system. This makes topology especially appropriate for the study of complex cognitive 
processes assumed to govern the morphogenesis that creates the "figure" of a text. 
Thus, the textual figure exists only as the result of cognitive processes and/or an 
mathematical abstraction of its viewpoints. This figure is free and independent of the 
surface features of text, but dependent on the language specific cues that carry the 
ecological information. Only through the cooperation of the viewpoints, carried by 
strings of symbols, and their schematizing can the mechanism inherent in natural 
language execute the relationship between observing and symbolizing in a meaningful 
way. This fact underpins the basic assumption of innate structural formation reflected 
through language. The dynamics of the transformational process involved and the 
constraints enforced by the terminal states create the topological order and con- 
sequently the synthetic concepts in correspondence with the given material. The way 
in which the different states are linked give rise to a course which characterizes the 
dynamics and structure of the original text. 

Figure 3 represents a three-dimensional space. The space (SxS) is indicated by 
the interval (s,<s-<s 4 ), while B, with the interval (b|<b.<b~), encompasses the be- 
havioural development of the process into a significant final state. By that, the process 
forms an attractor. The Space-Behaviour coordinates include a stable non-linear 
oscillating process and are therefore the natural choice of the Control space (C = 

S n xB) with coordinates (s,b). A point (c = (s ,b)) in C is called a control point and 

represents a particular topological invariant. C contains the entire bifurcation set (R ) 
with (r, <r.<r ). A bifurcation is a dividing point where a concealed operation in one 

type of description becomes visible in another. It also includes the one-dimensional 
variable (B) with coordinate (b-). The variable B represents the Behaviour space 

because it depicts the quantity which forms the cusp. The function from C to B is 
single valued. The dotted cusp lines form the surface of Figure 3. 

Applied to the Caption text, the (n = 2) clusters specify the terminal states that 
are required to specify the developmental process on the Visual Cliff. The variable for 
s 1 is 'The Glass Floor' and for s~ it is 'The Danger'. Moreover, they define the State 

space for the process. B is a distribution with a unique maximum at (b, ). It shows 

that the function represents the maximum of the curve in the single point (b, ) which 

also is the highest point of the cusp captured in the text. Thus, the attractor in the 
interval ^ <s~) has developed into a significant final state, marked by the singularity, 

called The Falling-off Place. 

It follows that the scientific problem now can be stated as the Figure of the text 
which is described by this singularity. Synthesis on the basis of the (AaO) formula is 
the reconstruction of the subject matter of analysis in a different, namely the 
topological dimension. In agreement with the formula (7) the Schema as generative 
process unfolds the mentality governing language production in correspondence with 
the analytical content of the language produced. This is the dynamical aspect of the 
(AaO) paradigm 



30 

Figure 3. 

Behaviour Space: Nonlinear Homorhesic Process Unfolding into a Helical structure. 




t 



31 



which is most amazing, because an unexpected arising consciousness can be discussed 
in a natural way. Consciousness can with Sperry (1966) be characterized as dynamic 
patterns which control language behaviour. These patterns effect a course which not 
only is bound to the texture but is anchored in the mentality. The creation and 
production of text logically must create "emergent novelties" (Rosen, 1978, pp. 90- 
93). 

In general, any consciousness that can be formulated into text would be an 
expression of an intentional act. There is no need for further reference to any specific 
underlying mechanism. It is postulated that the quality in the verbal expression is 
defined by its underlying Schema. As outlined in Figure 3, the synthetic concept The 
Falling-off Place is part of the theoretical expression in that, it designates a terminus 
or a limit and thus a topological invariant and this invariant allows an immediate 
translation of its mathematical property back into the Gibsonian theory of direct 
perception. 

The Perspective on the Figure 

The transformational process, originating in Table 1, shows that two textual 
agents have operated. The first one, agent ('X'), has governed the viewpoints 
associated with 'The Glass Floor' and is therefore profiled or typified with the help of 
this concept. It can easily be observed (Tab. 1) that this agent in a systematical way is 
related to the problem of coordinating sight and body movement reflected by the first 
textual string. The second textual string refers to the experimental environment, hence, 
the reference to a material being placed flush against the undersurface of the glass. 
Thus the first group of viewpoints refers to a device that could simulate for the infant 
the experience of falling. If this is the case, the result would be a Visual Cliff. With 
knowledge of the experimental context it is now possible to substitute the variable (X) 
with experimenter or with text producer because the experimenters are also the authors 
of the paper that appeared in Scientific American. 

The second group consists of textual strings that are related to that part of the 
experimental setting which gives the impression of depth. Therefore, it simulates the 
danger of falling. The agent ('he'), has governed the viewpoints associated with 'The 
Danger'. Thus, the pronoun 'he' can now be substituted with child. Consequently, the 
agent can be typified with the name of the second grouping which is "The Danger". 
The systematical relation of this agent with the cluster means that it concerns the 
ability to develop judgment in relation to the problem of coordinating sight and body 
movement. In conclusion, substitution of an unknown for a known agent can be 
carried out if and only if the affinity relations underlying the agent and objective 
configuration have been analyzed. 

Thus far, it can be summarized that the perspective puts the viewer into the 
Visual Cliff pictures. Gaining objective scientific knowledge requires the extraction of 
the perspective, because the perspective of the viewer represents the subjective 
inference and distortions brought about by subjectivity of the text producers. The 
observed structure of the Figure component is concerned with the perception of an 
edge, but this does not result in a better representation of reality nor does it enhance 
the reality of the picture series. The analysis is concerned with eliminating or at least 
minimizing subjectivity in order to gain in objectivity. An edge in itself does not 
imply that the observer conceives the ecological significant information nor does it 
imply that the edge has to be perceived as a call for action. 



32 



The Ground 

It is obvious that locomotion involving the Visual Cliff as point of orientation 
is the necessary prerequisite for the detection of the transformational invariant which 
specifies the nature of change on the floor. Gibson (1979, p. 157) writes: 

"A cliff is a feature of the terrain, a highly significant special kind of dihedral angle in 
ecological geometry, a falling-off place. The edge at the top of a cliff is dangerous. It 
is an occluding edge. But it has the special character of being an edge of the surface of 
support, unlike the edge of a wall. One can safely walk around the edge of a wall but 
not off the edge of a cliff. To perceive a cliff is to detect a layout but more than that, it 
is to detect an affordance, a negative affordance for locomotion, a place where the 
surface of support ends." 

Obviously, the Figure of the Caption to the picture series presents the scientific 
problem, namely direct perception of an abrupt change in the surface of support. 
Moreover, the text is intended to describe what affordance an abrupt change has for 
the child. In the Caption, meaning has been defined by relating the cliff to avoidance 
behaviour. 

Both real and virtual environments require a ground. The ground structures the 
observer's perception of objects and events. Reasoning by the experimenters means 
stating the ground for visual perception or imagination. However, in natural discourse 
the reason for behavioural orientation may be more or less structurally given and ex- 
tractable. Grouping the viewpoints of the Ground component means partly the 
empirical definition of a minimal grouping, partly the application of the same t-test 
criterion as in the identification of the groupings of the Figure component. The 
clustering of the binary matrix (k.) of the Ground component has resulted in the 

following dendrogram data: 



Cycle 

1 
2 
3 
4 
5 
6 
7 
8 



1 
1 

1 
1 
2 
8 
2 
1 



3 
4 
5 
7 
6 
9 
8 
2 



Coeff . 

0.000 
0.000 
0.000 
0.000 
0.400 
0.400 
0.400 
1.111 



Items grouped 

134572689 
I I I 

- I 

I I 

I 



I 



Mean = 0.289 
Dev. = 0.378 



Predicted Clusters = 2 
Realised Deviates =2.13 



(t 



80 



< 3.01 < t 



90 



33 



The process of concentrating the viewpoints of the Ground component starts from the 
empirical grouping of nine viewpoints. On the basis of the shred-test, two groups of 
textual strings carrying the viewpoints emerge: 

Group 1 

1. on the visual cliff 

3. across a sheet of heavy glass 

4. beneath the glass on one side and several feet below it on the other 

5. on the centre board (top left) 

7. from the 'deep' side 

Group 2 

2. of a board 

6. to its mother across the shallow side (top right) 

8. in fact a solid surface 

9. over to the mother (bottom right) 

The first group consists of five textual strings. Prototypical for all of them is 
that they help to determine a floor which has been experimentally modified in order to 
simulate the cliff. No doubt, the prototypical character of the first group relates to the 
awareness of depth and thus the possible detection of a negative affordance for lo- 
comotion, i. e. the discovery of "a place, where the surface of support ends". 
Consequently, the first cluster can be named 'The Detection of Negative Affordance'. 

The second group refers to information that can be picked up from the solid 
side of the glass floor. In this case the surface can both be seen and felt. It is this group 
of strings that carry the information about the solidity of the glass surface. The 
experimenters reason for this has been to study the child's ability to test the glass 
surface for its solidity. Thus, the second group represents the 'Surface of Support'. 
Both groups contribute to the definition of the surface conditions: a visible and an 
invisible side. Gibson (1979, p. 157) writes: 

"The glass affords support under both conditions but provides optical information for 
support only under the first. There is mechanical contact with the feet in both cases 
but optical information for contact with the feet only in the first." 

The structured configuration concerns the judgment of the consequences of 
locomoting on the deep side. Obviously, the transformational impact of the second 
group on the first gives expression to the experimenters reasons: Avoidance. It is 
inferred that the child is afraid of falling off the cliff. Thus, the result of an optical 
information processing can be measured sensibly only on the basis of propriospecific 
information. Gibson (1979, p. 157) writes: "One's body in relation to the ground is 
what gets attention." 

Perception and proprioception are complementary (Gibson, 1979, p. 157). This 
fact can be observed when the analysis of the Caption text takes its point of departure 
in the Schema model. The strict dependency between the textual elements becomes 
visible. Different agents have different functions in the text development and have 
been chosen to give expression to what is conscious to the experimenters. 

A differential typological analysis of the functioning of the agents will give 
information about which processes may be thought to operate in the manifestation of a 



34 



focused perspective. The grouping of the Agents associated with the viewpoints of the 
Ground (matrix k~) has resulted in the following computer output: 



Cycle 

1 
2 
3 

4 

Mean : 
Dev. = 



2 3 

2 4 

2 5 

1 2 

0.400 
0.356 



Coeff . 

0.222 
0.222 
0.222 
0.933 



Items grouped 



12 3 4 5 

I I I 

- I 

I I 

I 



Predicted Clusters = 2 
Realised Deviates = 1.50 



(t .80 < 2 ' 12 < fc , 



90 



) 



Two natural groups of Agents can be observed. The first contains one textual string 
(X). The second group consists of the other strings: 

Group 1 

1. X 

Group 2 

2. the apparatus 

3. the child 

4. despite this tactual evidence that the 'cliff 

5. he 

The systematic covariation of the first Agent group with the viewpoints (1, 3, 4, 5, 7) 
addressing 'The Detection of Negative Affordance' (matrix k.) clarifies the experi- 
menters stated reason: Measurement of the perception of the affordance of the layout 
through the judgment of a sharp drop by the child. Apparently, the researchers' aim is 
to learn more about how infants become aware of the meaning of a sharp drop. The 
agents of the second group are meaningfully related to the viewpoints (2, 6, 8, 9) 
implying 'Surface of Support', because the focus is here on alternative locomotion. To 
run the experiment, there has to be some action function. The apparatus and the child 
are required to provide for locomotion and for behavioural orientation across the cliff. 
Obviously, the Ground is the absolute axis of reference and marks distance as an 
extension along the floor. The Ground gives the operational definition of the 
viewpoints that denote the points of orientation. This is the implication of a focus on 
alternative possibilities for locomotion. 

In sum, the authors of the Caption text have been successful in realizing their 
purpose of describing the picture series of the Visual Cliff experiment from a theo- 
retical point of view. The topological analysis shows that the Figure component 
represents the significant environmental change, defined over the contrasting sides of 
the experimental layout. In order to bring out the theoretical important aspect of the 
theory of ecological perception, the results point toward a description by the 



35 



horizontal contrasting of pairs of pictures. But the Ground of the text must have been 
described by a vertical contrasting of the picture pairs, because the latter contrast gives 
evidence to avoidance as the other theoretical constituent of the experiment. 



Single Subject Experiment 

Perceivable events are defined by their discontinuities. Whether a certain event 
defines a risky environment depends on the structure of its affordance. A negative af- 
fordance, as in the Visual Cliff example, implies the detection of the ecological 
significance of discontinuous support. For example, many parents, who have carefully 
observed their infants at crawling age, may have noticed that initially they crawl over 
edges of different kind without being aware of the risk of falling. The design of a 
child's environment therefore has a decisive influence on its cognitive development. 
The adult has to exercise "prospective" control which means that the adult's ability to 
overlook a child defines its security range. Overlooking a child's activity comprises a 
covariation of physical experience and perceptual integration of the environment. But 
not before this integration is expressed symbolically can consciousness be observed. 
Symbolizing means that properties and phenomena, relations and connections, pro- 
cesses and consequences can be named and expressed as text. This ability is highly 
dependent on the adults own exposure to environmental change and shifting of 
perspective which has as its consequence that the function of viewpoints is changing. 

Method 

In general, any single subject's ability to relate itself to the event on the Visual 
Cliff has to be determined on the parameters characterizing the individual's level of 
performance and variability in performance. Strictly speaking, it is always appropriate 
to test the hypothesis of perspective and objective structure on the basis of a single 
subject experiment. Moreover, such an experiment is required if one wants to 
substantiate the conclusions drawn from the results of the analysis of the Caption text. 
Moreover, this kind of experiment needs no further legitimating, because it is the only 
defendable approach to schematizing processes. The individual's point of observation 
and angle of inclination determines position and distance to the event on the Visual 
Cliff. What from one observation point is perceived as an objective may be an inten- 
tion from another. 

Subjects. Since the original Visual Cliff experiments have been carried out 
with infants of crawling age as subjects, parents of infants of the same age were 
invited to participate. The parent was picked from a sample of sixteen who were 
booked for a routine control at a rural district's Child Care Centre. 

Materials. The parent were required to make as exact observations as possible 
on the pictures series of the Visual Cliff and to formulate these observations into a 
narrative. It is assumed that a verbalization in close connection to the pictures 
materializes the subject's particular orientation. This would imply that the viewpoints 
are intentionally chosen and the perspective is contained in the verbal flow. 

Design and Procedure. The subject were given orally the task to describe the 
content of the four pictures so as to make somebody get a conception of them who has 
not seen them. Further, information was given of (1) how to identify the glass surface, 
since this cue in the pictures (bottom left) has not been properly perceived as far as the 
pretest could show and (2) how to regard the picture series so as to make possible to 
conceive the pictures as a conceptual whole. 



36 



Data. The task was to produce a written narration. Ecological significance 
means that the infant's behaviour on the Visual Cliff may be taken as an indication that 
the environment "afford" something for the child. When our experimental subject is 
able to study the infant's purposeful behaviour and to express it wordly, the result 
should be a text reflecting these "affordances". The kind of text produced has been 
analyzed by means of the presented formalism. 

Results 

The Schema approach must be capable of not only controlling the 
organizational layout of the viewpoints and their variations in type and complexity but 
it must also control the perspective chosen. Moreover, this intertwined logic of 
analysis and synthesis must cope with the affordance and abstract its invariants on the 
basis of language specific variables. This ecological orientation presupposes that the 
coordination of body movement and visual ability can be developed and measured 
through changes of the viewpoints. Since these are supposed to be interacting with and 
dependent on changes in the perspective, it is interesting to study the outcome of what 
the experimental subject has picked up from the experimental set-up. 

Figure 4 represents the subject's Phase space (R xT) with (tQ<t,<tA The time 

interval encompasses the development of the process into conceptual depth. The pro- 
cess depicted is of a transformational kind. It transits through a number of states and 
produces at each progressive step a singularity as its response. The singularities are 
represented by the nodes on the enclosed part of the surface. It is a Phase space which 
is the result of any successive state's transformational effect on the immediately 
preceding state or singularity. The transformational process is metaphoric and as such 
asymmetric in kind. When the process moves inward, i.e. two phases cross each other, 
a more deeply embedded and thus a more elaborate mental structure emerges. If the 
course of the process changes direction and moves outward, this structure looses in 
embedding. 

The attractor in the interval (r,<r.<r^) develops smoothly as a stable 

oscillating process. Though two different paths develop in (r>) and (rA Both imply 

two short jumps, i. e. a hysteresis which is initiated by sudden changes in direction. 
When the third path crosses the second one a new and deeper embedded attractor 
comes into existence at (t~) . Still deeper embedded in the unfolding helical structure 

is the highest point of the curve which is the singularity at (t,). 

The perspective transformation of the depicted course can be achieved through 
the Agent control. The strict dependency of the matrices established by the (AaO) 
formula is most critical for observing what is in the focus of the perspective. The 
structured configuration of the Agents (in case it can be established) in relation to the 
configuration of the viewpoints can be comprehended topologically. 

The working of the Agent control is described precisely by a pendulum, whose 
movements are constraint by the way in which the groupings of the Agents are linked. 
Figure 5 gives the resting point of the pendulum. It is the highest point of its curve, 
namely the singularity where the process bifurcates. For example, by swinging the 
pendulum from state (s 7 ) to state (s^) the first invariant of the perspective {cA 

becomes available. By swinging the process back and force between states and 
singularities the process establishes the focus. Moreover, the transformational 
restructuring of the viewpoint-related agents implies the detection of structural 



Figure 4. 

Phase Space: Hysteresis 



37 







38 



invariants that do not specify an identity between the structure of the perspective on 
the Figure and the structure of the Figure itself, though occasionally structural 
identity may result. 

As indicated by Figure 4 the occurring structure is not dependent on the 
number of state variables. Their number may be large compared to the controlling 
attractors which are five. Dotted cusp lines symbolize the nonlinearity of the process. 

The problem now is to collapse the topological dimensionality such that the 
whole process can be represented on the surfaces of a cube. For that purpose, the 
movement of the process is marked with a circle around any singularity resulting from 
an inward move. If the course of the process moves outward, the structure looses in 
depth and corresponding circles are removed. 

The following convention has been established. The edge of the background 
surface of the cube represents the Phase space (P) of the Figure component, with 
(Pj<p-<p ) progressive steps. Any singularity (P •) produced by the steps is 

represented by a node on the surface. The focus of the perspective on the Figure is 
mapped onto the foreground surface of the cube. 

In order to achieve a compact representation the bottom of the cube and its top 
are used to map the Ground component correspondingly. For the other components, if 
they emerge as a structured configuration, the surfaces of the left and right hand side 
may be used as well as a projected surface beside the background. 

Processing of Exterospecific Information 

The surfaces of the cube (Fig. 5) reflect the compact topographic 
representation of narration of the event on the Visual Cliff by the experimental 
subject. Clearly, the Figure component of the cube shows five distinct phases. The 
first phase starts with 'Attention' and ends in the singularity of Awareness. Thus, the 
environmental condition is conceived as an awareness-experiment providing for the 
study of a child's ability to become aware of the pertinence of change. The second 
phase picks up the information related to the textural surface and is terminated in 
Physical Attraction. Speaking in Gibsonian terms, the hight has not yet been associ- 
ated with affordance. The third phase concerns the child's Ego-orientation. A change 
in perspective is enforced through a 'Lure' which results in the singularity Emotional 
Attraction. The implication of this is an Ego-motion toward the 'Lure'. When the third 
phase crosses the second one, a fourth phase comes into existence and ends in Equivo- 
cation. It indicates that our experimental subject has identified two different kinds of 
attraction and perceived their competing difference. Moreover, the terminus is deeper 
embedded in the unfolding cognitive structure. 

An apparent problem in the narration of the Visual Cliff experiment by this 
subject has resulted from the function of the Lure'. This is clearly brought out when 
the fourth phase crosses the first one. The fifth and final singularity is marked with 
two circles. They indicate a further deepening of the cognitive structure. The 
attractiveness of the Lure' for the infant has been conceptualized as a confounding 
factor. This "uncleanness" of the original Visual Cliff experiment consequently results 
in Distress as the root of the Figure, i.e a stressful situation for the child. One of the 
subcomponent shows that the subject was able to detect and narrate environmental 
change as defined over the two contrasting sides. The other subcomponent represents 
the observed transformation of locomotion through the Lure' into egomotion. In- 



39 



Figure 5. 

Topographical Representation of a Narrative of the Event on the Visual Cliff 



Reconnoitering 
Behaviour 

Support 

Visual Field 



Attention 



Subject \ 



Placement 
Responsiveness 
Appearance y^ Cue 



Ego-Orientation 



Lure 



Awareness 



Power of Influence 




Deep Side 

Shallow Side 
Ego-Orientation 




Focussing 

Reaction 

Distress 
i 

Awareness 

Equivocation 
i 

Physical Attraction 
Emotional 
Attraction 




Surface 

Visual Field 

Reconnoitering 
Behaviour 



Stimulation 

Appearance 

Responsiveness 



40 



tentional egomotion transforms into provocation, which has to be conceived as 
"cognitive motion". 

Processing of Propriospecific Information 

With reference to the theory of ecological perception, it is important to 
separate the structure of the Figure from the structure of the perspective if one wants 
to study the child's reaction to its environment. Therefore, the analysis of a symbolic 
expression cannot be carried out successfully before the focus of the textual per- 
spective is experimentally detached from its viewpoints. The model developed rests on 
its capability to determine the Agent function, i.e. the perspective, which governs the 
choice of viewpoints in the language production. Perspective control lies in the 
functional definition of the agents and the viewpoints. Identifying and isolating the 
agents effect implies that "propriospecific" (Gibson, 1979, p. 157) becomes available. 
The process of concentrating this information consists of directing the analysis toward 
an iterative process that determines the minimally sufficient groups that represent the 
whole configuration of agents. The purpose of differentiating the textual agents into 
salient groups on the basis of the prototypes found in the analysis of the viewpoints is 
to identify the agents who have the same profile of scores on these viewpoints. 

The focus is on the stressful situation. Moreover, the subject's perspective 
constitutes a transformation which brings the appearance of the experiential layout and 
the child's responsiveness into focus. Perspective transformation of the Figure 
component produces what reported experimental outcomes give evidence for. Some 
infants who have reached an early crawling age (5-9 months) would give emotional 
expression to the provocation by crying toward their mother (Gibson & Walk, 1960). 

Processing the Reason for Experiential Information 

The Ground component provides complementary information. The subject 
seems to reason about what the Gibson and Walk experiment could actually show. The 
Ground represents possible forces of attraction while the course of the process 
specifies the child's Responsiveness with respect to the optical arrangement as its root. 

The focus of the perspective on the Ground makes clear that the behavioural 
event is what has come into view. Obviously, "Ego-motion" is encompassed in Ego- 
orientation. Moreover, the results make evident: The experimental subject refuses to 
state the affordance of the perceived, i.e. to state the Gibsonian inference. The reason 
for the event on the cliff and consequently, with respect to the child, the reason for the 
realism of the negative affordance cannot be established. 

Discussion 

Thus, there is very little reason to doubt the preciseness and completeness of 
natural language when used in a scientific as well as in natural context. The 
metaphoric properties of language allow people to communicate information put into 
perspective which is always unambiguous. By the metaphoric use of language it is 
therefore required the natural, and not the semantically based ability to conceptualize. 

The crucial assumption behind this presentation is that the world can be 
perceived when the medium for reflecting its structural qualities are the conceptual 
relations lying in the texture of natural language expressions. But the structure of a 
certain event cannot be demonstrated independently of theory. The Gibsonian theory 
of affordance is based on the Kantian schema and provides the necessary theoretical 
link. Accordingly, events that have affordances have ecological significance. The 
affordance properties of significant events are characterized by a structure which has 









41 



to be specified by a model whose components are assumed to collaborate in order to 
attain or conserve the relations of the structure. 

But the transient nature of the event requires its description in technical terms. 
Only a technical specification can make visible and possibly avoid conceptual am- 
biguity. Thus, the course of events and consequent action strategies have to be defined 
through laboratory operations (experiment and measurement). The series of pictures of 
the Visual Cliff experiment presents such a definition. The pictured procedure gives a 
formal expression to a child's experience of a provocation. The persisting invariants of 
the discovered structure give evidence to a stressful situation that is the result of the 
ambiguous definition of perceptual integration and synthesis. 

Gibson and Walk (1960) have produced a Caption text to the picture series that 
contains the theoretical important singularities, namely the imagination of "The 
Falling-off-Place", i. e. a virtual cliff and "Avoidance" as its behavioural ground. 
Though, the negative affordance is unconsciously inferred. The operationalization of 
the theoretical objective in the form of the pictured organizational layout is not the 
primary information provider for the our experimental subject. Consequently, their is 
no clear support for a prospective reference, i.e. direct perception of depth and the 
development of meaning as related to the judgment of consequences. In conclusion, 
the parent of a child in crawling stage is able to make conscious the insignificance of 
the pictured event for a theory of affordance. 

References 

Anderberg, M. R. (1973). Cluster analysis for applications. New York: Academic 
Press. 

Ball, W., & Tronick, E. (1971). Infant responses to impending collision: Optical and 
real. Science, 171, 818-820. 

Becker, J. D. (1973). A model for the encoding of experiential information. In R. C. 

Schank, & K. M. Colby (Eds.), Computer models of thought and language (pp. 
396-434). San Fransisco: Freeman. 

Bierschenk, B. (1981). Conceptions of cognitive functions in a science of knowing 
(Didakometry, No. 63). Malmo, Sweden: Lund University, School of 
Education. 

Bierschenk, B. (1984). The split between meaning and being (Kognitionsvetenskaplig 
forskning, No. 3). Lund, Sweden: Lund University, Department of 
Psychology. 

Bierschenk, B., & Bierschenk, I. (1986 a). Analyse der Sprache in Ver- 

haltenssimulierung (Analysis of language in behaviour simulation). In W. 
Langthaler & H. Schneider (Eds.), Video-Ruckmeldung und Verhaltenstraining 
(Video-feedback and behaviour training) (pp. 63-102). Minister, Germany: 
MAkS Publications. 



42 



Bierschenk, B., & Bierschenk, I. (1986 b). Concept formulation. Part II. Measurement 
of formulation processes (Kognitionsvetenskaplig forskning, No. 11). Lund, 
Sweden: Lund University, Department of Psychology. (ERIC Document 
Reproduction Service No. ED 275 159, TM 01 1 260) 

Bierschenk, I. (1987). The controlling function of the agent in the analysis of question- 
response relationships (Kognitionsvetenskaplig forskning, No. 19). Lund, 
Sweden: Lund University, Department of Psychology. (ERIC Document 
Reproduction Service No. ED 295 945, TM 010 264) 

Bierschenk, I. (1989). Language as carrier of consciousness (Kognitionsvetenskaplig 
forskning, No. 30). Lund, Sweden: Lund University, Department of Psychol- 
ogy. (ERIC Document Reproduction Service No. ED 312 645, TM 014 033) 

Cassirer, H. W. (1970). A commentary on Kant's critique of judgment. London: 
Methuen. 

Cattell, R. B. (1966). Handbook of multivariate experimental psychology (pp. 174- 
243). Chicago: Rand McNally. 

Danzig, T. (1968). Number. The language of science. London: George Allen & 
Unwon. 

Everitt, B. (194). Cluster analysis. London: Heinemann. 

Foerster, H. (1969). What is memory that it may have hindsight and foresight as well? 
In S. Bogoch (Ed.) The future of the brain sciences. Proceedings of a con- 
ference held at the New York Academy of Medicine, May 2-4 (pp. 19-87). New 
York: Plenum Press. 

Frisch, K. (1967). The dance language and orientation of bees. Cambridge, MA: The 
Belknap Press of Harvard University Press. 

Gibson, E. J., & Walk, R. D. (1960). The visual cliff. Scientific American, 202, 64-71. 

Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton 
Mifflin. 

Gibson, J. J., Kaplan, G. A., Reynolds, H., & Wheeler, K. (1969). The change from 
visible to invisible: A study of optical transitions. Perception and 
Psychophysics,5, 113-116. 

Hartman, R. S. (1967). The structure of value: Foundations of scientific axiology. 
Carbondale and Edwardsville: Southern University Press. 

Helmersson, H. (1987). Texteditering och klusteranalys vid perspektivisk textanalys. 
Version 1.1 (Editing of text and cluster analysis in perspective text analysis. 
Version 1.1) Unpublished manuscript. 



43 



Helmersson, H. (1991). Pertex (Computer program). Lund, Sweden: Lund University, 
Department of Business Administration. 

Jaynes, J. (1976). The origin of consciousness in the breakdown of the bicameral 
mind. Boston: Houghton Mifflin. 

Kant, I. (1975). Die drei Kritiken in ihrem Zusammenhang mit dem Gesamtwerk (The 
three critiques together with their connection to the complete edition). 
Stuttgart, Germany: Alfred Kroner Verlag. 

Kugler, P. N., & Turvey, M. T. (1987). Information, natural law and the self- 
assembly of rhythmic movement. Hillsdale, NJ: Erlbaum. 

Lorenz, K. (1941). Kants Lehre vom Apriorischen im Lichte der gegenwartigen 
Biologie (Kant's doctrine of the a prioristic in the light of present biology). 
Blatter fur deutsche Philosophy, 15, 94-125. 

Minsky, M. (1975). A framework for representing knowledge. In P. H. Winston (Ed.), 
The psychology of computer vision (pp. 211-280). New York: McGraw-Hill. 

Pattee, H. H. (1977). Dynamic and linguistic modes of complex systems. International 
Journal of General systems, 3, 259-266. 

Pattee, H. H. (1980). Clues from molecular symbol systems. In U. Bellugi & M. 

Studdert- Kennedy (Eds.), Signed and spoken languages. Biological constraints 
of linguistic form. (pp. 261-273). Weinheim: Verlag Chemie. 

Polanyi, M., & Prosch, H. (1975). Meaning. Chicago: University of Chicago Press. 

Piaget, J. (1978). Behaviour and evolution. New York: Pantheon Books. 

Regan, D., Beverley, K., & Cynader, M. (1979). The visual perception of motion in 
depth. Scientific American, 241, 136-151. 

Rosen, R. (1978). Fundamentals of measurement and representation of natural 
systems. New York: North-Holland. 

Saunders, P. T. (1980). An introduction to catastrophe theory. Cambridge: Cambridge 
University Press, 1980. 

Sokal, R., & Sneath, P. H. (1963). Principles of numerical taxonomy. San Fransisco: 
Freeman. 

Sperry, R. W. (1952). Neurology and the mind-brain problem. American Scientist, 40, 
291-312. 

Sperry, R. W. (1966). Mind, brain and humanistic values. Bulletin of the Atomic 
Scientist, 22, 2-6. 



44 



Sperry, R. W. (1969). A modified concept of consciousness. Psychological Review, 
76, 532-536. 

Tinbergen, N. (1951). The study of instinct. Oxford: Oxford University Press. 

Ward, J. H.. (1963). Hierarchical grouping to optimize an objective function. Journal 
of the American Statistical Association, 58, 236-244. 

Wigner, E. P. (1967). Remarks on the mind-body question. In W. J. Moore & M. 
Scriven (Eds.), Symmetries and reflections: Scientific essays of Eugene P. 
Wigner (pp. 171-184). Westport: Greenwood Press. 

Wishart, D. (1982). Clustan: User manual (Inter-University Research Council Series 
No. 47). Edinburgh: Edinburgh University, Program Library Unit.